Suppose the particle travels from W to Y along the path WXZY as shown. Compare t

Question

Suppose the particle travels from W to Y along the path WXZY as shown. Compare the work done by the electric field when the particle travels from point W to point X to that done when the particle travels from point Z to point Y. Explain. What is the total work done on the particle by the electric field as it moves along the path WXZY? Suppose the particle travels from W to Y along the arc shown. Is the work done on the particle by the electric field positive, negative, or zero? Explain using force and displacement vectors.

Explanation / Answer

Here ,

1. the work done by the electric field is given aa

work done = - change in potential energy

Now , due to a two charges potential energy is given as

energy = k * q1 * q2/distance

hence , for both ZY and WX , magnitude of work done will be same

but as the charge is moving in oposite direction , the sign will be oposite. Hence ,

W(ZY/W(WX) = -1

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for the total work done ,

as the points W and Y are at same distance from the middle charge.

total work done = 0 .(as change in potential energy = 0)

2.
for the arc ,

as the potential due to a point charge is given as

V = k * q/d

hence , WY is a equipotential surface , and work done ob the particle by the electric field is ZERO

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